## Geometric Computing with Clifford Algebras: Theoretical Foundations and Applications in Computer Vision and RoboticsClifford algebra, then called geometric algebra, was introduced more than a cenetury ago by William K. Clifford, building on work by Grassmann and Hamilton. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "mother algebra" in various subfields of physics and engineering. Recent work outlines that Clifford algebra provides a universal and powerfull algebraic framework for an elegant and coherent representation of various problems occuring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics. This monograph-like anthology introduces the concepts and framework of Clifford algebra and provides computer scientists, engineers, physicists, and mathematicians with a rich source of examples of how to work with this formalism. |

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### Contents

New Algebraic Tools for Classical Geometry | 3 |

Generalized Homogeneous Coordinates | 27 |

Spherical Conformal Geometry with Geometric Algebra | 61 |

A Universal Model for Conformal Geometries | 77 |

GeoMAP Unification | 105 |

Honing Geometric Algebra for Its Use in the Computer | 127 |

Algebraic Embedding of Signal Theory and Neural | 153 |

E RundbladLabunets | 155 |

Clifford Algebra Multilayer Perceptrons | 315 |

Geometric Algebra for Computer Vision and Robotics | 335 |

3DReconstruction from Vanishing Points | 371 |

Analysis and Computation of the Intrinsic Camera | 393 |

CoordinateFree Projective Geometry for Computer | 415 |

The Geometry and Algebra of Kinematics | 455 |

Kinematics of Robot Manipulators | 471 |

Using the Algebra of Dual Quaternions for Motion | 489 |

Noncommutative Hypercomplex Fourier Transforms | 187 |

Commutative Hypercomplex Fourier Transforms | 209 |

Fast Algorithms of Hypercomplex Fourier Transforms | 231 |

Local Hypercomplex Signal Representations | 255 |

Introduction to Neural Computation in Clifford Algebra | 291 |

The Motor Extended Kalman Filter for Dynamic Rigid | 501 |

References | 531 |

532 | |

543 | |

### Common terms and phrases

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### References to this book

Lectures on Clifford (Geometric) Algebras and Applications Rafal Ablamowicz,Garret Sobczyk Limited preview - 2004 |